Design of input shapers for suppressing vibrations in the Z-plane

Input shaping technique is well used for reducing residual vibrations of flexible systems. However, the strategies of both the time domain and the vector diagram are complex to improve the robustness of an input shaper. Zero placement method in the z-plane is utilized to design multi-hump robust input shapers. Two or more shaper zeros are placed nearby the system pole to work out the typical symmetric multi-hump input shapers conveniently. Furthermore, the design strategy can also be used to design unsymmetric input shapers and the shapers which are robust to both modeling frequency and damp ratio. This design strategy is easier to derive and implement. Application in the anti-swing control of overhead cranes verified the fine performance of this strategy. A better suppression of the load vibrations is obtained using the proposed new multi-hump input shapers, which are more robust to the variation of the cable length